Before his posting in Geneva, Vangelis was Ambassador to the European Union, NATO and Sweden based in Brussels and has had postings to Canberra as Deputy High Commissioner and before that in Moscow. From 2008-2011 Vangelis was the Chief Negotiator who led the conclusion of the regional ASEAN-Australia-New Zealand Free Trade Agreement (FTA) and the separate FTA with Malaysia. He was also part of the negotiating teams for the FTA with China and the precursor to the Trans-Pacific Partnership Agreement, the Pacific-Four FTA. Vangelis is also the Chief Negotiator for the (currently suspended) FTA negotiations with the Customs Union of Armenia, Belarus, Russia, Kazakhstan and Kyrgyzstan.‎

Vangelis has worked outside the Ministry, including at the Organisation for Economic Cooperation and Development (OECD) from 2001-2004. Prior to his work in the OECD Secretariat, Vangelis was a member of a team of economists which helped develop a partial equilibrium model to assess the possible impact of Russia's WTO accession on its agriculture sector. He has also worked with the Republics of Uzbekistan and Turkmenistan on similar issues, including their WTO accession processes.